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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 16560.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16560.d1 | 16560o2 | \([0, 0, 0, -8643, -254558]\) | \(47825527682/8926875\) | \(13327752960000\) | \([2]\) | \(36864\) | \(1.2364\) | |
16560.d2 | 16560o1 | \([0, 0, 0, 1077, -23222]\) | \(185073116/419175\) | \(-312912460800\) | \([2]\) | \(18432\) | \(0.88986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.d have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.d do not have complex multiplication.Modular form 16560.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.